The market demand for a particular good in city A is given by Q(A) = 32...

The market demand for a particular good in city A is given by Q(A) = 32 ? 0.5P (for P ? 64). This market is served by a single firm (monopoly) whose marginal cost of production is 4 dollars per unit (so total cost of producing Q units is 4Q).

(a) Find the equation for the firm’s marginal revenue function. Draw the demand, marginal cost and marginal revenue curves on one graph.

(b) What are the profit-maximizing price and quantity for the monopolist?

(c) Calculate the monopoly profit and mark-up in city A.

(d) What is consumer surplus in this market? How large is the deadweight loss resulting from monopoly pricing?

Expert Solution

Market demand function is Q = 32 – 0.5P or inverse demand function is 0.5P = 32 – Q or P = 64 – 2Q

a) Now we have P = 64 – 2Q. Total revenue function is TR = 64Q – 2Q^2. Marginal revenue is the derivative of TR so MR = 64 – 4Q

b) Monopolist equates MR = MC

64 – 4Q = 4

Q = 60/4 = 15 units and so monopolist charges a price of 64 – 2*15 = $34 per unit.

c) Profit = TR – TC = 15*34 – 4*15 = 15*30 = $450. Mark up = (P – MC)/P = (34 – 4)/34 = 0.88

d) CS = 0.5*(Max price – current price)*current qty = 0.5*(64 – 34)*15 = $225

DWL = 0.5*(34 – 4)*(30 – 15) = $225

Rahul Sunny answered 2 years ago

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